Invariance Under Scaling of Time Bounds in Timed Discrete-Event Systems

by S.E. Bourdon, W.M. Wonham, and M. Lawford

Abstract: A family of affine maps on the time bounds for discrete-event systems is introduced. It is shown that unless these affine maps are in fact linear, then the timed activity transition graph (TATG) of an arbitrary timed discrete-event system (TDES) may not be preserved under the scaling operation. Moreover, it is shown that when the scaling is linear, the TATG is always preserved under scaling. We examine some applications of the result, including state space reduction and make connections to suboptimal supervisory controller synthesis and dense time scaling. Finally, we briefly discuss topics for future study including the extensions to model-checking and efficent representation of TDES.

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BibTeX Entry

@InProceedings{BoWoLa:00,
  author = 	 {S.E. Bourdon and W.M. Wonham and M. Lawford},
  title = 	 {Invariance under scaling of
time bounds in discrete-event systems},
  booktitle = 	 {Proceedings of the 38th Annual
Allerton Conference on Communication, Control, and Computing},
  pages = 	 {1145-1154},
  year = 	 {2000},
  volume = 	 {2}
}